How to get from imaginary to real chemical potential

TL;DR

This paper demonstrates how analyzing the effective potential at imaginary chemical potential in the Gross-Neveu model allows reconstruction of the full phase diagram at real chemical potential, emphasizing the importance of analytical continuation of the effective potential.

Contribution

It shows that the phase diagram of a relativistic quantum field theory can be fully recovered from imaginary chemical potential data by focusing on the effective potential, including inhomogeneous phases.

Findings

Full phase diagram can be obtained from imaginary chemical potential analysis.

Analytic continuation of the effective potential is essential.

Inhomogeneous phases require the full effective action computation.

Abstract

Using the exactly solvable Gross-Neveu model as theoretical laboratory, we analyse in detail the relationship between a relativistic quantum field theory at real and imaginary chemical potential. We find that one can retrieve the full information about the phase diagram of the theory from an imaginary chemical potential calculation. The prerequisite is to evaluate and analytically continue the effective potential for the chiral order parameter, rather than thermodynamic observables or phase boundaries. In the case of an inhomogeneous phase, one needs to compute the full effective action, a functional of the space-dependent order parameter, at imaginary chemical potential.